1. Field of the Invention
The present invention relates generally to spacecraft attitude control.
2. Description of the Related Art
Spacecraft attitudes are typically controlled with attitude-control structures that are each capable of generating an individual spacecraft momentum vector. A plurality of these individual momentum vectors vectorially combine to form a composite momentum vector which urges spacecraft rotation about the composite vector.
FIG. 1 illustrates a typical body-stabilized spacecraft 20 whose attitude can be defined relative to an orthogonal coordinate system 22 that has an origin at the spacecraft's center of mass. The coordinate system 22 has a yaw axis 24 which is directed from the origin towards a point on a celestial body, e.g., the Earth 26. A pitch axis 28 is orthogonal to the spacecraft's orbital plane 30 and a roll axis 32 is aligned with the satellite's velocity vector. As the body-stabilized satellite 20 orbits the Earth 26, its yaw axis 24 typically rotates so that it is constantly directed at the Earth's center of mass.
Solar cell arrays 34 and 35 typically extend from the spacecraft so that they can rotate about the pitch axis 28 to enhance their exposure to the Sun. Antennas (e.g., the antennas 36 and 37) are usually directed towards the Earth for communication and thrusters (e.g., monopropellant, bipropellant and electrostatic) are carried on the spacecraft's body 40 to facilitate stationkeeping and attitude control. Although thrusters 42 and 43 can be carried on various body faces, they are canted from the antinadir face 44 in this exemplary spacecraft.
Positioning one of the thrusters 42 and 43 so that its thrust line is spaced from the spacecraft's center of mass and firing this thruster will generate a torque in the spacecraft 20 that urges it to rotate relative the coordinate system 22. The enlarged view of FIG. 2 illustrates that a torque can also be generated in the spacecraft 20 by appropriately positioning those spacecraft structural members which are exposed to solar radiation 50. For example, rotating the solar arrays 34 and 35 to be respectively orthogonal and parallel to the solar radiation 50 will generate a torque that urges the spacecraft 20 to rotate in the direction of the rotation arrows 52.
A magnetic torquing coil 56 can be carried in the spacecraft body 40 so that it is exposed to magnetic flux lines 58 of a celestial body (e.g., the Earth 26 of FIG. 1). Passing an electrical current through the coil 56 causes the magnetic field to generate a force on the coil that, in turn, urges the spacecraft 20 to rotate relative to the coordinate system 22.
More versatile attitude-control structures are formed with rotating members that generate angular momentum which can be oriented to produce a selected momentum vector. Increasing the angular velocity of such members imparts a torque into a spacecraft which urges it to rotate about the selected momentum vector in an angular direction opposite that of the rotating member. In contrast, decreasing the angular velocity of such members urges the spacecraft to rotate in the same angular direction as that of the rotating member.
An exemplary rotating member is a momentum wheel which typically rotates in one direction and stores momentum for accumulation (by rotating faster) or release (by rotating slower). Reaction wheels are similar to momentum wheels but rotate in both directions so that their momentum states include the zero momentum state. A momentum wheel or reaction wheel that is gimbaled to facilitate changes in its momentum direction is conventionally referred to as a control moment gyroscope. The term "momentum wheel" will hereinafter be generically used to refer to any rotating-member structure in which at least one of its momentum and its momentum direction is selectable.
In a momentum wheel set 60 of FIG. 2, momentum wheels 62, 64 and 66 are arranged to rotate respectively about the roll axis 32, the pitch axis 28 and the yaw axis 24 of the coordinate system 22. When the momentum wheel 66 rotates in the angular direction 68, it generates a momentum vector 70 that is directed along the positive yaw axis. Reversing the wheel's rotation causes a reversal of the momentum vector. If the momentum wheels 62, 64 and 66 are rotated to respectively generate the momentum vectors 72, 74 and 76 of FIG. 2, these vectors will vectorially add to a composite momentum vector 80 in the spacecraft 20. The vectorial addition is indicated by broken lines 82 which indicate orthogonal projection lines. The spacecraft 20 is thus urged to rotate about the composite momentum vector 80 in FIG. 2.
Because space is three dimensional, a minimum of three attitude-control structures is required to realize commanded momentum vectors. Three attitude-control structures form a uniquely-determined attitude-control system because there is only one unique combination of three momentum vectors that will realize a commanded momentum vector. For example, there is only one combination of angular velocities of the momentum wheels 62, 64 and 66 that generates the momentum vector 80.
In contrast, four or more attitude-control structures form an over-determined attitude-control system in which an infinite combination of momentum vectors can be found to realize a commanded momentum vector. As an example, adding a backup roll-axis momentum wheel 82 or a skew momentum wheel 84 changes the momentum wheel set 60 from a uniquely-determined attitude-control system to an over-determined attitude-control system. Because the rotational axis of the skew momentum wheel 84 is not orthogonal with any coordinate axis, it can also serve as a failure backup for any of the momentum wheels 62, 64 and 66.
Adding any other attitude-control structure (e.g., the torquing coil 56, the solar cell arrays 34 and 35 or the thrusters 42 and 43 of FIG. 1) also changes the momentum wheel set 60 from a uniquely-determined attitude-control system to an over-determined attitude-control system. Another over-determined attitude-control system 90 is shown in FIG. 3. This system has four momentum wheels 92, 94, 96 and 98 whose rotational axes are aligned along the edges of an imaginary pyramid 99 (e.g., an equilateral pyramid). An exemplary use of an over-determined attitude-control system can be found in U.S. Pat. No. 5,058,835 which is directed to momentum-wheel speed management.
Although momentum wheels are versatile attitude-control structures, they typically have imperfections (e.g., wheel imbalance, bearing flaws, and cyclic electromagnetic effects) that impart disturbance torques into a spacecraft. When the frequency of one of these disturbance torques substantially equals the frequency of a resonance in a spacecraft structure (e.g., a solar cell array or an antenna), this disturbance torque is magnified and the resulting attitude error degrades the performance of sensitive spacecraft equipment (e.g., optical sensors and multi-spectral sensors).
The probability of exciting a structural resonance is significant because momentum wheels typically exhibit a plurality of disturbance torques whose frequencies are generally proportional to the momentum wheel's speed and spacecraft structures typically exhibit a plurality of resonances. The excitation problem is further complicated because the frequencies of spacecraft resonancs are oftentimes not known.
Conventional approaches to the reduction of disturbance torques have involved the use of passive vibration-isolation platforms, ultra-precise wheel balancing, active wheel suspension techniques (e.g., with magnetic bearings) and active vibration suppression (e.g., with piezoelectric actuators). These approaches, however, are typically complex, expensive, use spacecraft weight and volume and often have limited effectiveness.